luckadjusted

Week 17 2023 · December 31, 2023

Bengals at Chiefs, Week 17 2023: who deserved to win?

The Chiefs beat the Bengals 25–17, and it was no fluke: replayed with the way both teams actually played, the Chiefs win 9 of 10.

Before kickoff the Chiefs were 71% favorites. The biggest swing (Q2, 10:53 left): the Chiefs were stopped on 3rd & 7, worth 15 points of win probability to the Bengals.

Final

Cincinnati Bengals 17
Kansas City Chiefs 25

December 31, 2023 · GEHA Field at Arrowhead Stadium · Closing line: Chiefs −7.5

Luck index +11 Chiefs about even · −11 Bengals

Each team’s own plays from this game, resampled into new drives 4,000 times: with the way both teams actually played, how often does this performance win? How the replay works

Ten replays. Bengals win 1, Chiefs win 9.

  1. 1 CIN 20 KC 13
  2. 2 CIN 20 KC 23
  3. 3 CIN 14 KC 20
  4. 4 CIN 7 KC 16
  5. 5 CIN 13 KC 24
  6. 6 CIN 17 KC 30
  7. 7 CIN 10 KC 26
  8. 8 CIN 12 KC 31
  9. 9 CIN 0 KC 24
  10. 10 CIN 16 KC 47

Three other ways to ask

Each answers a different question, so none of them replaces the replay above.

The closing betting line, turned into a probability. What everyone knew before the game.

The line plus what this game showed, weighted by how much one game can tell. It stays close to the line because one game says little.

Every kick, fumble bounce, drop, conversion and judgment call redrawn; everything else fixed. The narrowest view of luck.

How 4,000 replays ended

Bengals win 11% of them, Chiefs 89%, counting the 2% still level after regulation as half each. The line is what actually happened: Chiefs by 8.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+0.6%
Bengals by 9–162.5%
Bengals by 1–87.0%
Level after regulation1.7%
Chiefs by 1–818.2%
Chiefs by 9–1623.9%
Chiefs by 17+46.1%

Where the luck was

What the luck was worth

Every lucky and unlucky play, weighted by the moment it happened: its swing in win probability, added up by kind. A missed kick in a decided game counts for nothing; the same kick at the end of a tie game can be most of a win.

Swings add up across a game, so in one that went back and forth they can pass 100%. On the scoreboard the same luck was worth +0.5 points to the Bengals: the final margin was Chiefs by 8, without the luck Chiefs by 8.5. Luck shares are the fitted ones (how much of each kind is luck).

The kicks

How likely each kicker was to make that kick (his own record, the distance and the weather), and what happened.

  • E. McPherson, 34 yds made · 92% expected
  • H. Butker, 54 yds made · 60% expected
  • H. Butker, 43 yds made · 79% expected
  • H. Butker, 27 yds made · 98% expected
  • H. Butker, 24 yds made · 99% expected
  • H. Butker, 48 yds made · 72% expected
  • H. Butker, 46 yds made · 76% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 3 for 20 yards, Chiefs 3 for 39 yards

Every accepted flag, in order, and what it did to the helped team’s chance of winning at that moment, including any play it wiped out (points on the scoreboard in grey). A flag in a decided game is worth nothing; one at the turn of a close game can be worth most of a win. Judgment calls count toward luck, pre-snap fouls mostly don’t. How calls are valued

WhenFlagWin probability for
Q1 9:49 Ineligible Downfield Pass on the Bengals, 5 yards, wiping out the play +10% KC +2.1 pts
Q2 7:21 Defensive Pass Interference on the Chiefs (L'Jarius Sneed), 4 yards +4% CIN +1.6 pts
Q2 1:52 False Start on the Chiefs, 5 yards · pre-snap +3% CIN +0.7 pts
Q3 10:02 Defensive Pass Interference on the Chiefs (Joshua Williams), 30 yards +10% CIN +3.4 pts
Q3 6:42 Defensive Holding on the Bengals (Sam Hubbard), 5 yards 0% KC +0.5 pts
Q4 6:18 Intentional Grounding on the Bengals, 10 yards +3% KC +0.9 pts

Bengals penalties, every game · Chiefs penalties, every game · All teams, 2023

When it happened

Chiefs’ chance of winning

As low as 21% and as high as 100%. Numbers mark the biggest luck moments, listed below.

nflfastR’s in-game win probability. It ignores the betting line, so it starts near even. Shaded above the middle while the Chiefs were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 9:49 Ineligible Downfield Pass on the Bengals, 5 yards, wiping out the playJudgment calls +10% KC KC: Touchdown
2 Q1 8:42 The Bengals converted 3rd & 73rd & 4th downs · 32% expected +9% CIN CIN: Field goal
3 Q2 10:53 The Chiefs were stopped on 3rd & 73rd & 4th downs · 38% expectedThe Chiefs fumbled and the Bengals recoveredFumble bounces · loose balls are close to 50/50 +15% CIN KC: Field goal
4 Q2 0:44 The Chiefs were stopped on 3rd & 33rd & 4th downs · 56% expectedM. Valdes-Scantling dropped a catchable passDrops · 6 drops on 89 catchable balls before this +13% CIN KC: Field goal
5 Q3 10:02 Defensive Pass Interference on the Chiefs (Joshua Williams), 30 yardsJudgment calls · 6 flags in 1275 snaps before, position avg 1 per 216 +10% CIN CIN: Turnover on downs
6 Q3 7:47 The Bengals were stopped on 4th & 13rd & 4th downs · 65% expected +14% KC CIN: Punt
7 Q3 7:00 The Chiefs converted 3rd & 43rd & 4th downs · 50% expected +12% KC KC: Field goal
8 Q4 15:00 The Chiefs were stopped on 3rd & 33rd & 4th downs · 47% expected +9% CIN KC: Field goal

Missing players

Key players (usually on the field for half the snaps or more) who missed this game or part of it, valued by position and quality. The same players are missing in every replay, so this counts as luck in points only.

  • Donovan Smith (KC T), out · 1.2 pts
  • Bryan Cook (KC FS), out (IR) · 0.3 pts
  • Skyy Moore (KC WR), out (IR) · 0.2 pts
  • Joe Burrow (CIN QB), out (IR), replaced by j.browning · 3.8 pts
  • D.J. Reader (CIN NT), out (IR) · 0.3 pts

Adjust the assumptions

Disagree with how much of a fumble bounce or a pass interference call is luck? Change it and the coin-flip replay reruns in your browser.

Only coin-flips re-rolled

Bengals 7% · Chiefs 93%

Final margin
Chiefs by 8
Luck in points
0.5 for the Bengals
Luck-adjusted margin
Chiefs by 8.5
Replay with same day's form
Bengals 11% · Chiefs 89% unchanged: why
How much of each is luck?

0% treats it as skill, 100% as pure luck. The tick is our fit.

What counts

We tested momentum on 19,000 lucky breaks and found none, so it's off by default. Why

Flip a play

Force the other outcome, in this game and in every replay: a made kick becomes a miss, a stop becomes a conversion, a flag goes the other way.

About these numbers

Play-by-play and win probability from nflfastR via nflverse; kicks valued against each kicker’s own record; drops and interception-worthy throws from FTN charting; injuries from snap counts and injury reports.

Methodology and validation · All Week 17 2023 games · Bengals · Chiefs

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